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Lesson 1 (Unit Rates)

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• Lesson 1 (Unit Rates)

1. 1. Name Numeracy Skill Builder: Long Division Write any remainders as fractions and reduce. Date 3 25 8 506 6 1227 4 8030 Objectives 1. Find a Unit Rate 2. Compare by using Unit 1 1 1 1 Rates 8 63 204 2007 3 4 2 2 Concept 1: Find a Unit Rate Basic Proficient Advanced I need 24 dollars for 6 sandwiches. I need 18 cups of flour for 8 loaves of I need 2 teaspoons of salt for 60 Find and reduce the unit rate. bread. Find and reduce the unit rate. cookies. Find and reduce the unit rate. 1 1 4 dollars per sandwich 2  cups per loaf  teaspoon per cookie 4 30 Concept 2: Compare by using Unit Rates Basic Proficient Advanced Andrew drives 150 miles in 4 hours. Andrew drives 120 miles in 2 hours. Andrew drives 228 miles in 4 hours. How fast does he drive? Erika drives 196 miles in 3 hours. Erika drives 281 miles in 5 hours. Who drives faster? Who drives faster and by how much? 1 1 1 A : 60 mph E : 65  mph A : 57 mph E : 56  mph 37  miles per hour 3 5 2 4 Erika drives faster. Andrew  drives faster by mph 5
2. 2. How fast does he drive? Erika drives 196 miles in 3 hours. Erika drives 281 miles in 5 hours. Who drives faster? Who drives faster and by how much? Test Prep 3 Work / Explanation 1. Which number is the additive inverse of - ? 5 A 5 C 3 Additive inverse = opposite. - 3 5 ( )+( )=0 B - 5 D 3 Change the sign. 3 5 3 2. Which number is the multiplicative inverse of - ? 5 Multiplicative inverse = reciprocal. A 5 C 3 3 - 5 ( )•( )=1 B 5 D 3 Flip the fraction. - 3 5
3. 3. How fast does he drive? Erika drives 196 miles in 3 hours. Erika drives 281 miles in 5 hours. Who drives faster? Who drives faster and by how much? Test Prep 3 Work / Explanation 1. Which number is the additive inverse of - ? 5 A 5 C 3 Additive inverse = opposite. - 3 5 ( )+( )=0 B - 5 D 3 Change the sign. 3 5 3 2. Which number is the multiplicative inverse of - ? 5 Multiplicative inverse = reciprocal. A 5 C 3 3 - 5 ( )•( )=1 B 5 D 3 Flip the fraction. - 3 5
4. 4. How fast does he drive? Erika drives 196 miles in 3 hours. Erika drives 281 miles in 5 hours. Who drives faster? Who drives faster and by how much? Test Prep 3 Work / Explanation 1. Which number is the additive inverse of - ? 5 A 5 C 3 Additive inverse = opposite. - 3 5 ( )+( )=0 B - 5 D 3 Change the sign. 3 5 3 2. Which number is the multiplicative inverse of - ? 5 Multiplicative inverse = reciprocal. A 5 C 3 3 - 5 ( )•( )=1 B 5 D 3 Flip the fraction. - 3 5
5. 5. Which one should I buy?
6. 6. 24.12 ounces 36.5 ounces
7. 7. 24.12 ounces 36.5 ounces .331 24.12 7.99
8. 8. 24.12 ounces 36.5 ounces .331 24.12 7.99 Each ounce costs 33.1 cents
9. 9. 24.12 ounces 36.5 ounces .331 .247 24.12 7.99 36.5 8.99 Each ounce costs 33.1 cents
10. 10. 24.12 ounces 36.5 ounces .331 .247 24.12 7.99 36.5 8.99 Each ounce costs 33.1 cents Each ounce costs 24.7 cents
11. 11. 24.12 ounces 36.5 ounces .331 .247 24.12 7.99 36.5 8.99 Each ounce costs 33.1 cents Each ounce costs 24.7 cents
12. 12. 24.12 ounces 36.5 ounces .331 .247 24.12 7.99 36.5 8.99 Each ounce costs 33.1 cents Each ounce costs 24.7 cents
13. 13. Main Concept Unit Rates
14. 14. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. =
15. 15. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet =
16. 16. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet = 5 presents
17. 17. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet = 5 presents
18. 18. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet = 5 presents more or less than 1 whole?
19. 19. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet = 5 presents more or less than 1 whole? 5 8
20. 20. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet = 5 presents more or less than 1 whole? 1 5 8
21. 21. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet = 5 presents more or less than 1 whole? 1 5 8 −5
22. 22. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet = 5 presents more or less than 1 whole? 1 5 8 −5 3
23. 23. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet = 5 presents more or less than 1 whole? 3 1 5 8 −5 3
24. 24. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet = 5 presents more or less than 1 whole? 3 15 5 8 −5 3
25. 25. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet 3 = 1 5 presents 5 more or less than 1 whole? 3 15 5 8 −5 3
26. 26. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet 3 feet = 1 5 presents 5 present more or less than 1 whole? 3 15 5 8 −5 3
27. 27. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet 3 feet 3 = 1 = 1 5 presents 5 present 5 more or less than 1 whole? 3 15 5 8 −5 3
28. 28. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet 3 feet 3 = 1 = 1 feet per present 5 presents 5 present 5 more or less than 1 whole? 3 15 5 8 −5 3
29. 29. Find Unit Rate I run 3 miles in 21 minutes. =
30. 30. Find Unit Rate I run 3 miles in 21 minutes. 3 miles =
31. 31. Find Unit Rate I run 3 miles in 21 minutes. 3 miles = 21 minutes
32. 32. Find Unit Rate I run 3 miles in 21 minutes. 3 miles = 21 minutes
33. 33. Find Unit Rate I run 3 miles in 21 minutes. 3 miles = 21 minutes more or less than 1 whole?
34. 34. Find Unit Rate I run 3 miles in 21 minutes. 3 miles = 21 minutes more or less than 1 whole? 3 21
35. 35. Find Unit Rate I run 3 miles in 21 minutes. 3 miles = 21 minutes more or less than 1 whole? 3 ÷3 21
36. 36. Find Unit Rate I run 3 miles in 21 minutes. 3 miles = 21 minutes more or less than 1 whole? 3 ÷3 21 ÷3
37. 37. Find Unit Rate I run 3 miles in 21 minutes. 3 miles = 21 minutes more or less than 1 whole? 3 ÷3 1 = 21 ÷3 7
38. 38. Find Unit Rate I run 3 miles in 21 minutes. 3 miles 1 = 21 minutes 7 more or less than 1 whole? 3 ÷3 1 = 21 ÷3 7
39. 39. Find Unit Rate I run 3 miles in 21 minutes. 3 miles 1 mile = 21 minutes 7 minute more or less than 1 whole? 3 ÷3 1 = 21 ÷3 7
40. 40. Find Unit Rate I run 3 miles in 21 minutes. 3 miles 1 mile 1 = = 21 minutes 7 minute 7 more or less than 1 whole? 3 ÷3 1 = 21 ÷3 7
41. 41. Find Unit Rate I run 3 miles in 21 minutes. 3 miles 1 mile 1 = = mile per minute 21 minutes 7 minute 7 more or less than 1 whole? 3 ÷3 1 = 21 ÷3 7
42. 42. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? =
43. 43. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars =
44. 44. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months
45. 45. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months
46. 46. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months more or less than 1 whole?
47. 47. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months more or less than 1 whole? 3 400
48. 48. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months 1 more or less than 1 whole? 3 400
49. 49. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months 1 more or less than 1 whole? 3 400 −3
50. 50. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months 1 more or less than 1 whole? 3 400 −3 1
51. 51. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months 1 more or less than 1 whole? 3 400 −3 10
52. 52. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months 13 more or less than 1 whole? 3 400 −3 10
53. 53. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months 13 more or less than 1 whole? 3 400 −3 10 −9
54. 54. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months 13 more or less than 1 whole? 3 400 −3 10 −9 1
55. 55. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months 13 more or less than 1 whole? 3 400 −3 10 −9 10
56. 56. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months 13 3 more or less than 1 whole? 3 400 −3 10 −9 10
57. 57. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months 13 3 more or less than 1 whole? 3 400 −3 10 −9 10 −9
58. 58. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months 13 3 more or less than 1 whole? 3 400 −3 10 −9 10 −9 1
59. 59. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months 1 13 3 3 more or less than 1 whole? 3 400 −3 10 −9 10 −9 1
60. 60. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars 133 1 = 3 months 3 1 13 3 3 more or less than 1 whole? 3 400 −3 10 −9 10 −9 1
61. 61. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars 133 1 dollars = 3 months 3 month 1 13 3 3 more or less than 1 whole? 3 400 −3 10 −9 10 −9 1
62. 62. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars 133 1 dollars 1 = = 133 3 months 3 month 1 3 13 3 3 more or less than 1 whole? 3 400 −3 10 −9 10 −9 1
63. 63. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars 133 1 dollars 1 dollars per = = 133 3 months 3 month 1 3 month 13 3 3 more or less than 1 whole? 3 400 −3 10 −9 10 −9 1
64. 64. Find Unit Rate I need 3 cups of sugar for 2 cakes. Find the unit rate. I spend \$265 every 4 weeks. Find the unit rate. A tree grows 4 inches in 12 years. How fast is it growing? I drive 228 miles in 5 hours. How fast am I driving?
65. 65. Find Unit Rate I need 3 cups of sugar for 2 cakes. Find the unit rate. 1 1 cups per cake 2 I spend \$265 every 4 weeks. Find the unit rate. A tree grows 4 inches in 12 years. How fast is it growing? I drive 228 miles in 5 hours. How fast am I driving?
66. 66. Find Unit Rate I need 3 cups of sugar for 2 cakes. Find the unit rate. 1 1 cups per cake 2 I spend \$265 every 4 weeks. Find the unit rate. 1 66 dollars per week 4 A tree grows 4 inches in 12 years. How fast is it growing? I drive 228 miles in 5 hours. How fast am I driving?
67. 67. Find Unit Rate I need 3 cups of sugar for 2 cakes. Find the unit rate. 1 1 cups per cake 2 I spend \$265 every 4 weeks. Find the unit rate. 1 66 dollars per week 4 A tree grows 4 inches in 12 years. How fast is it growing? 1 inch per year 3 I drive 228 miles in 5 hours. How fast am I driving?
68. 68. Find Unit Rate I need 3 cups of sugar for 2 cakes. Find the unit rate. 1 1 cups per cake 2 I spend \$265 every 4 weeks. Find the unit rate. 1 66 dollars per week 4 A tree grows 4 inches in 12 years. How fast is it growing? 1 inch per year 3 I drive 228 miles in 5 hours. How fast am I driving? 3 45 miles per hour 5
69. 69. Comparing Quantities Samantha ran 96 meters in 40 seconds. Juan ran 110 meters in 50 seconds. Who ran faster?
70. 70. Comparing Quantities Samantha ran 96 meters in 40 seconds. Juan ran 110 meters in 50 seconds. Who ran faster? Samantha
71. 71. Comparing Quantities Samantha ran 96 meters in 40 seconds. Juan ran 110 meters in 50 seconds. Who ran faster? Samantha 96 meters = 40 seconds
72. 72. Comparing Quantities Samantha ran 96 meters in 40 seconds. Juan ran 110 meters in 50 seconds. Who ran faster? Samantha 96 meters 2 = 2 40 seconds 5
73. 73. Comparing Quantities Samantha ran 96 meters in 40 seconds. Juan ran 110 meters in 50 seconds. Who ran faster? Samantha 96 meters 2 = 2 meters per second 40 seconds 5
74. 74. Comparing Quantities Samantha ran 96 meters in 40 seconds. Juan ran 110 meters in 50 seconds. Who ran faster? Samantha 96 meters 2 = 2 meters per second 40 seconds 5 Juan
75. 75. Comparing Quantities Samantha ran 96 meters in 40 seconds. Juan ran 110 meters in 50 seconds. Who ran faster? Samantha 96 meters 2 = 2 meters per second 40 seconds 5 Juan 110 meters = 50 seconds
76. 76. Comparing Quantities Samantha ran 96 meters in 40 seconds. Juan ran 110 meters in 50 seconds. Who ran faster? Samantha 96 meters 2 = 2 meters per second 40 seconds 5 Juan 110 meters 1 = 2 50 seconds 5
77. 77. Comparing Quantities Samantha ran 96 meters in 40 seconds. Juan ran 110 meters in 50 seconds. Who ran faster? Samantha 96 meters 2 = 2 meters per second 40 seconds 5 Juan 110 meters 1 = 2 meters per second 50 seconds 5
78. 78. Comparing Quantities Samantha ran 96 meters in 40 seconds. Juan ran 110 meters in 50 seconds. Who ran faster? Samantha 96 meters 2 = 2 meters per second 40 seconds 5 Juan 110 meters 1 = 2 meters per second 50 seconds 5 They were very close, but Samantha ran faster by 1/5 of a meter every second.
79. 79. Comparing Quantities Noemi ran 105 meters in 30 seconds. Mirian ran 112 meters in 40 seconds. Who ran faster? My tomato plants grow 4 inches in 10 months. My pepper plants grow 3 inches in 6 months. Which grows faster? Francisco earned \$74 in 8 hours. Jasmine earned \$105 in 12 hours. Who has a better paying job?
80. 80. Comparing Quantities Noemi ran 105 meters in 30 seconds. Mirian ran 112 meters in 40 seconds. Who ran faster? 1 4 Noemi: 3  metersper second Mirian: 2  metersper second 2 5 My tomato plants grow 4 inches in 10 months. My pepper plants grow 3 inches in 6 months. Which grows faster? Francisco earned \$74 in 8 hours. Jasmine earned \$105 in 12 hours. Who has a better paying job?
81. 81. Comparing Quantities Noemi ran 105 meters in 30 seconds. Mirian ran 112 meters in 40 seconds. Who ran faster? 1 4 Noemi: 3  metersper second Mirian: 2  metersper second 2 5 My tomato plants grow 4 inches in 10 months. My pepper plants grow 3 inches in 6 months. Which grows faster? Francisco earned \$74 in 8 hours. Jasmine earned \$105 in 12 hours. Who has a better paying job?
82. 82. Comparing Quantities Noemi ran 105 meters in 30 seconds. Mirian ran 112 meters in 40 seconds. Who ran faster? 1 4 Noemi: 3  metersper second Mirian: 2  metersper second 2 5 My tomato plants grow 4 inches in 10 months. My pepper plants grow 3 inches in 6 months. Which grows faster? 2 1 Tomato:  inch per month Pepper:  inch per month 5 2 Francisco earned \$74 in 8 hours. Jasmine earned \$105 in 12 hours. Who has a better paying job?
83. 83. Comparing Quantities Noemi ran 105 meters in 30 seconds. Mirian ran 112 meters in 40 seconds. Who ran faster? 1 4 Noemi: 3  metersper second Mirian: 2  metersper second 2 5 My tomato plants grow 4 inches in 10 months. My pepper plants grow 3 inches in 6 months. Which grows faster? 2 1 Tomato:  inch per month Pepper:  inch per month 5 2 Francisco earned \$74 in 8 hours. Jasmine earned \$105 in 12 hours. Who has a better paying job?
84. 84. Comparing Quantities Noemi ran 105 meters in 30 seconds. Mirian ran 112 meters in 40 seconds. Who ran faster? 1 4 Noemi: 3  metersper second Mirian: 2  metersper second 2 5 My tomato plants grow 4 inches in 10 months. My pepper plants grow 3 inches in 6 months. Which grows faster? 2 1 Tomato:  inch per month Pepper:  inch per month 5 2 Francisco earned \$74 in 8 hours. Jasmine earned \$105 in 12 hours. Who has a better paying job? 1 3 Francisco: 9  dollars per hour Jasmine: 8  dollars per hour 4 4
85. 85. Comparing Quantities Noemi ran 105 meters in 30 seconds. Mirian ran 112 meters in 40 seconds. Who ran faster? 1 4 Noemi: 3  metersper second Mirian: 2  metersper second 2 5 My tomato plants grow 4 inches in 10 months. My pepper plants grow 3 inches in 6 months. Which grows faster? 2 1 Tomato:  inch per month Pepper:  inch per month 5 2 Francisco earned \$74 in 8 hours. Jasmine earned \$105 in 12 hours. Who has a better paying job? 1 3 Francisco: 9  dollars per hour Jasmine: 8  dollars per hour 4 4